The growth of the range of stable random walks

Wojciech Cygan, Nikola Sandrić, Stjepan Sebek

Research output: Contribution to journalArticle

Abstract

In this article, we establish an almost sure invariance principle for the capacity
and cardinality of the range for a class of α-stable random walks on the integer
lattice Zd with d > 5α/2 and d > 3α/2, respectively. As a direct consequence, we
conclude Khintchine's and Chung's laws of the iterated logarithm for both processes.
Original languageEnglish
Number of pages16
JournalarXiv.org e-Print archive
Publication statusSubmitted - 2019

Keywords

  • The range of a random walk
  • Capacity
  • An almost sure invariance principle
  • The law of the iterated logarithm

ASJC Scopus subject areas

  • Mathematics(all)

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